Analysis of a synchronization model in an anisochronous system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1408-1419 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A model system of two first-order differential equations that arises in the synchronization theory of nonlinear oscillations is investigated. Constraints on the parameters of the equations under which the synchronization is realized on every solution are found. A domain of the parameters in which the synchronization occurs only for a part of the solution set is determined.
@article{ZVMMF_2010_50_8_a5,
     author = {L. A. Kalyakin},
     title = {Analysis of a synchronization model in an anisochronous system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1408--1419},
     year = {2010},
     volume = {50},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a5/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - Analysis of a synchronization model in an anisochronous system
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1408
EP  - 1419
VL  - 50
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a5/
LA  - ru
ID  - ZVMMF_2010_50_8_a5
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T Analysis of a synchronization model in an anisochronous system
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1408-1419
%V 50
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a5/
%G ru
%F ZVMMF_2010_50_8_a5
L. A. Kalyakin. Analysis of a synchronization model in an anisochronous system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 8, pp. 1408-1419. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_8_a5/

[1] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[2] Blekhman I. I., Sinkhronizatsiya v prirode i tekhnike, Nauka, M., 1981 | MR | Zbl

[3] Pikovskii A., Rozenblyum M., Kurts Yu., Sinkhronizatsiya. Fundamentalnoe nelineinoe yavlenie, Tekhnosfera, M., 2003

[4] Andronov A. A., Vitt A. A., Khaikin S. E., Teoriya kolebanii, Fizmatgiz, M., 1959

[5] Slavin A., Tiberkevich V., “Nonlinear auto-oscillator theory of microwave generation by spin-polarized current”, IEEE Trans. Magnetics, 45:4 (2009), 1875–1918 | DOI

[6] Adler R., “A study of locking phenomena in oscillators”, Proc. IRE, 34 (1946), 351–357 ; Rept Proc. IEEE, 61(10) (1973), 1380–1385 | DOI | DOI

[7] Barenblatt G. I., Podobie, avtomodelnost, promezhutochnye asimptotiki, Gidrometeoizdat, L., 1978 | MR

[8] Denisov S. I., Lyutyy T. V., Hanggi P., Trohidou K. N., “Dynamical and thermal effects in nanoparticle systems driven by a rotating magnetic field”, Phys. Rev. B, 74 (2006), 104406/1–104406/8 | DOI

[9] Kalyakin L. A., Shamsutdinov M. A., “Adiabatic approximations for Landau–Lifshitz equations”, Proc. Steklov Inst. Math., 2007, S1–S17

[10] Kalyakin L. A., “Asimptoticheskii analiz modelei avtorezonansa”, Uspekhi matem. nauk, 63:5 (2008), 3–72 | MR | Zbl

[11] Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, VINITI, M., 1985